The term Peer to Peer is an umberella, promoted by the publisher OReilly to cover a number of phenomena.

In essence, the idea is that the web, as it developed during the 1990s, followed a kind of star shaped or client-server architecture. Central servers offered people services : information or shopping; and most people on the net were clients of these services. Indeed, the software run by the servers was different from the software run by the clients (typically a browser like Netscape or Internet Explorer) which reinforced the character of two roles.

But by the beginning of the new millenium, observers noticed a new wave of uses of the internet that started moving away from this pattern towards a more genuinely distributed network of peers. These applications formed a diverse list :

applications like Seti@Home which allowed users to turn their computers into components of large information processing projects

Instant Messaging

Although the applications were very different, they shared an common architectural features. Users entered into individual relations with other users. Both used the same software package and had equivalent capacities.

ClayShirky hit on a fortuitous way of understanding the commonality. All these applications made it easier to address the resources at the edge of the net. Instant messaging identified people at edge machines not central email accounts, file sharing made music files on edge machines available for download from other edge machines. Seti@Home made the processing power of edge machines available.

Sometimes theses services required centralized servers to put these edge nodes in touch with each other; but suddenly the edge constituted a huge pool of untapped resources which P2P applications could get at.

Wireless networking is creating a more distributed internet where messages hop from one cell of the wireless network to another rather than go via the telephone system to a central exchange. (Of course, due to geography, the network of overlapping radio "lillypads" will never be highly connected, but is likely, especially in dense urban areas to produce a network apparently free of central exhanges / routers.)

Maybe even the most succesful dotcom : eBay is more P2P than most, allowing users to sell their stuff to each other.